STABILITY ANALYSIS OF DRUG ABUSE TRANSMISSION DYNAMICS

Authors

  • Abqorry Zakiyyah Andalas University
  • Susila Bahri Andalas University

DOI:

https://doi.org/10.25077/jmua.14.1.103-116.2025

Keywords:

Mathematical Modelling, Drug Abuse Transmission, SLARS Model

Abstract

This research introduced a nonlinear deterministic model known as SLARS (Susceptible, Light Users, Addicted, and Reformed Users) along with a stability analysis to investigate the dynamics of drug abuse transmission. The basic reproduction number (R0) was calculated using the next-generation matrix method. Following this, the study examined the local stability of both the drug abuse-free and endemic equilibrium points. The findings indicated that when R0 is below 1, the drug abuse-free equilibrium point is locally stable. In contrast, when R0 is greater than 1, the endemic equilibrium point shows local stability. Additionally, simulation results supported the analytical conclusions of the study.

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References

J. Ahmad, U.C. Joel, F.O. Talabi, O.N. Bibian, A.B. Aiyesimoju, V.O. Adefemi, V.C. Gever, textit{Impact of social media-based intervention in reducing youths’ propensity to engage in drug abuse in Nigeria}, Evaluation and program planning, textbf{94} (2022), 102--122.

J.R. Branan, E. William, textit{Differential Equations: An Introduction to Modern Methods and Aplication}, Wiley, New York, 2015.

O. Diekmann, J.A.P. Heesterbeek, M.G. Roberts, textit{The construction of next generation matrices for compartmental epidemic models}, J. R.Soc. Interface. textbf{7} (2010), 873--885.

L. Edelstein-Keshet,textit{Mathematical Models in Biology}, Random House, New York, 2008.

R. L. Evans, N.O. JoAnn, textit{COVID-19 Pandemic: World in Turmoil}, Train Education, California, 2022.

Herindrasti, V.L. Sinta, textit{Drug-free ASEAN 2025: Challenges for Indonesia in Combating Drug Abuse}, International Relations Journal, textbf{7(1)} (2018), 19--33.

I. Kabbash, O. Zidan, S. Saied, textit{ Substance abuse among university students in Egypt: Prevalence and correlates}, Eastern Mediterranean Health Journal, textbf{28(1)}(2022), 31--40

W.G. Kelley, A.C. Peterson, textit{The Theory of Differential Equations Classical and Qualitative Second Edition}, Springer, New York, 2010.

Imron, Masyhuri et al, textit{2019 Drug Abuse Prevalence Survey}, National Narcotics Board, Jakarta, 2020.

B.P. Machhi, J.E Magar, S.S. Mishra, K.A. Salauddin, K.R. Manawarali, M.L.K.A. Vyas, textit{Review on current increases of drug abuse among teenagers}, Research Chronicler, textbf{10(2)} (2022), 58--71.

S. Mushayabasa and G. Tapedzesa, textit{Modeling illicit drug use dynamics and its optimal control analysis}, Computational and Mathematical Methods in medicine, (2015), https://dx.doi.org/10.1155/2015/383154.

National Institute on Drug Abuse, {it Drugs, brain, and behavior: the science of addiction}, (3rd edition), National Institute on Drug Abuse National Institutes of Health, Rockville MD, 2007.

National Narcotics Board of Republic of Indonesia, textit{Indonesia Drugs Report 2022}, National Narcotics Board, Jakarta, 2022.

B. Susila, F. Indah, N. Hamidah, L. Riri, F. Lili, textit{Analysis of the effects of foreign travelers and immigrants on omicron transmission in Indonesia}, International Journal of Mathematics and Computer Science, textbf{19} (2024), 893-902.

L, Stephen, textit{Dynamical system with application using mathematics}, Birkhauser, Boston, 2017.

BPS-Statistics Indonesia, textit{Statistical Yearbook of Indonesia}, BPS-Statistics Indonesia, Jakarta, 2022.

E. White and C. Comiskey, textit{Heroin epidemics, treatment and ode modeling}, Mathematical Biosciences, textbf{208} (2007), 312 -- 324.

Our editor speaking at the PKP conference.

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Published

31-01-2025

How to Cite

Zakiyyah, A., & Bahri, S. (2025). STABILITY ANALYSIS OF DRUG ABUSE TRANSMISSION DYNAMICS. Jurnal Matematika UNAND, 14(1), 103–116. https://doi.org/10.25077/jmua.14.1.103-116.2025

Issue

Vol. 14 No. 1 (2025)

Section

Articles

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